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“I was disappointed in listening to the President as he’s saying, ‘Oh Republicans are waging a war on women,’” Romney said at a Wednesday campaign rally in Hartford, an event painstakingly choreographed to flaunt Romney’s robust female support base. “The real war on women is being waged by the President’s failed economic policies.”

Romney’s campaign has been obsessing over this point in recent days, disseminating what looks like a damning statistic across every possible medium: 92.3% of the jobs lost during Obama’s tenure belonged to women. That figure, if you calculate it the way the Romney campaign does, is technically accurate. But it’s also incredibly misleading. The labor force participation rate for women is actually near its historical high and the recession, if anything, was a little harder on men.

How do we reconcile these facts? The recession started before Obama took office. In its first months, the hardest hit sectors were male-dominated like construction, which tanked because of a devastated housing sector. (You remember, the “mancession.”) But later, after Obama took office, the losses began to spread to different areas of employment, the big one being state governments, whose revenue intake was decimated by the crash. Public sector losses took some time to catch up (austere state budgets were passed in 2009 and 2010), but when they did, they comprised the long tail of unemployment dragging down the recovery until the end of last year. Many of those losses affected teaching, a profession dominated by women. That’s why Romney’s figure shows a disproportionate number of job losses among the fairer sex. (You can read much more about this subject here, replete with excellent charts.)

There’s a political flaw in Romney’s talking point, too: It’s very hard for him to argue he would have been able to do better just for women. Given the above explanation for the gender discrepancy, an effective women-targeted policy prescription would have involved greater state aid–stimulus, in the generic political parlance–something that Republicans generally oppose. The left-leaning outlet Talking Points Memo reports the Romney campaign did not have a response when asked what Obama could have done differently. The main reason: it would have involved taking a decidedly un-Republican position. (Romney also walked into a nasty scrape when his campaign wasn’t immediately sure if he supported Obama’s Lilly Ledbetter Fair Pay Act, which would make it easier for women to sue over compensation discrimination. Romney now says he does support it, but it was mostly opposed by the GOP and one of the congresswomen standing beside him onstage Wednesday voted against it. )

So why try so hard to make a gender-specific argument? It might seem obvious: Democrats have been aggressively making the case that the GOP is carrying out a nefarious “war on women,” seeking to deny them free contraception (Republicans support a broad “conscience clause” exemption to allow employers to opt out of providing coverage under a new mandate from the Department of Health and Human Services), abortions (Romney wants to withdraw federal funds for Planned Parenthood, which provides a range of women’s health services), and unfettered access to reproductive health (a number of Republican state legislatures have passed prerequirements for obtaining an abortion, such as receiving an ultrasound or hearing a description of the fetus). Young, secular women in particular may be a key swing group in November, and Romney is staring down a yawning gender gap in the polls: A recent USA Today/Gallup survey found him trailing Obama by 18 points among female voters.

There’s a catch though. In that widely cited poll, most Americans had no idea what Republicans or Romney’s positions on contraception were. He’s emerging bruised, perhaps more so than any other candidate in recent history, from his presidential primary fight. But he still has a compelling argument to make, one that pretty much every poll suggests can be effective, and it’s not that Obama’s economic policies failed women in particular. It’s that Obama’s economic policies failed everyone. Romney is already making this argument, and the two are not mutually exclusive. But why contort himself to score points on one side of the gender divide? “A rising tide lifts all boats” would be the relevant cliche in this case. More women plan out household budgets than men. They’re concerned about gas prices and job stability. Romney knows all this. That’s why he’s making an economic argument and not a cultural one. But there’s simply no need to overreach with misleading statistics.

You could go one step further. Refighting the Culture Wars is not an appealing prospect for most Americans, especially in times of economic distress. This was, in fact, something that dogged Republicans during their primary. So Romney could be out there telling voters that Democrats are trying to distract them from more important issues. As political jujitsu goes, that has some potential to be effective. Romney’s argument that Obama’s economic policies disproportionately hurt women does not.